Best architecture to learn image rotation?
This would likely suffer from the blurry image problem that autoencoders are known to suffer from. See also here.
On the other hand, using GAN's to sharpen your images doesn't seem particularly helpful since you seem to be lookng for a way to rotate general images, not ones of a specific domain. Moreover, there's almost certainly going to be some loss

It seems unreasonable/overkill to use neural networks to do this transformation. I suggest treating the rotation as a linear transformation, mapping certain pixel locations to other pixel locations (in fact, you can make this transformation differentiable with respect to its inputs using some deep learning library's autodifferentiation tools, if that's what you're looking for).
Since rotations are just linear maps that send pixels to other pixels, this will be much more computationally efficient.